“He is in the mix, but there are others in the mix,” a senior administration official told CBS on Thursday, referring to Barr. “There are a lot of people at the White House who would like for him to be the pick but ultimately it is up to the one person.”

Barr served as America’s chief law enforcement officer under President George H. W. Bush, who died late last week, from 1991 to 1993. If nominated and confirmed by the Senate, the longtime Republican lawyer, who also held deputy and assistant attorney general posts during Bush’s administration, would be the permanent successor to Jeff Sessions, who abruptly resigned as attorney general in early November at the request of President Trump.

Because he has been leading the department on an acting basis, Whitaker would need senate approval if he is nominated for the permanent attorney general post. Such a confirmation process would likely be deeply contentious as Democrats have repeatedly criticized Mr. Trump for appointing Whitaker, who has never held a senate-confirmed position and who has publicly denounced the special counsel’s investigation into Russian meddling in U.S. elections.

Whitaker assumed oversight of Robert Mueller’s far-reaching probe when he was appointed as acting attorney general. While some some have discounted Whitaker over of some of the controversy that has trailed him before he was picked in this interim capacity, he remains very viable. Sources inside and outside the administration say there have been times when his appointment as acting attorney general has been described by Mr. Trump as “rent to own.”

A senior administration official told CBS News that Barr would be “an easy confirmation” because of his background and experience in Washington politics.

Some in the White House, however, are concerned that Barr represents the GOP’s moderate, establishment wing and that he lacks a personal relationship with Mr. Trump. The new attorney general is likely to have oversight of the special counsel’s inquiry, which is also investigating possible ties and coordination between Trump campaign associates and the Kremlin.

According to the Washington Post, Barr has been critical over the attorneys Mueller has picked for his team. Barr told the newspaper that “prosecutors who make political contributions are identifying fairly strongly with a political party” and added, “I would have liked to see [Mueller] have more balance on this group.”

Mr. Trump’s attorney general pick could be announced as quickly as this week or within the next couple weeks according to White House sources. Even if Barr or another pick is announced by the president quickly it would still take months before the selection would be confirmed.

The senior administration official noted that nothing is final until Mr. Trump makes a final decision.